{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "915d13af",
   "metadata": {},
   "source": [
    "## Finding and Hedging Portfolio Beta Using Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6b68701b",
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install statsmodels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "87f6a032",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "from IPython.display import Markdown, display\n",
    "from openbb import obb\n",
    "from statsmodels import regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0cbacf37",
   "metadata": {},
   "outputs": [],
   "source": [
    "obb.user.preferences.output_type = \"dataframe\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8ae5043",
   "metadata": {},
   "source": [
    "Define the stock symbols including the benchmark \"SPY\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0ad36b85",
   "metadata": {},
   "outputs": [],
   "source": [
    "symbols = [\n",
    "    \"NEM\",\n",
    "    \"RGLD\",\n",
    "    \"SSRM\",\n",
    "    \"CDE\",\n",
    "    \"LLY\",\n",
    "    \"UNH\",\n",
    "    \"JNJ\",\n",
    "    \"MRK\",\n",
    "    \"SPY\",\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6eb4574",
   "metadata": {},
   "source": [
    "Fetch historical price data for the defined symbols from 2020-01-01 to 2022-12-31 using the \"yfinance\" provider"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f42846d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = obb.equity.price.historical(\n",
    "    symbols,\n",
    "    start_date=\"2020-01-01\",\n",
    "    end_date=\"2022-12-31\",\n",
    "    provider=\"yfinance\",\n",
    ").pivot(columns=\"symbol\", values=\"close\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6eada077",
   "metadata": {},
   "source": [
    "Calculate the daily percentage returns for the benchmark \"SPY\" and drop any missing values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3d11bbaf",
   "metadata": {},
   "outputs": [],
   "source": [
    "benchmark_returns = data.pop(\"SPY\").pct_change().dropna()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec5d9063",
   "metadata": {},
   "source": [
    "Calculate the daily percentage returns for the portfolio and drop any missing values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "545dca50",
   "metadata": {},
   "outputs": [],
   "source": [
    "portfolio_returns = data.pct_change().dropna().sum(axis=1)\n",
    "portfolio_returns.name = \"portfolio\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97db70eb",
   "metadata": {},
   "source": [
    "Plot the portfolio and benchmark daily returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e35eb93e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "portfolio_returns.plot()\n",
    "benchmark_returns.plot()\n",
    "plt.ylabel(\"Daily Return\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f290aad",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "source": [
    "Define a function for linear regression to calculate alpha and beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3f3968ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "def linreg(x, y):\n",
    "    # Add a column of 1s to fit alpha\n",
    "\n",
    "    x = sm.add_constant(x)\n",
    "    model = regression.linear_model.OLS(y, x).fit()\n",
    "    # Remove the constant now that we're done\n",
    "\n",
    "    x = x[:, 1]\n",
    "    return model.params[0], model.params[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "344a3b78",
   "metadata": {},
   "source": [
    "Perform linear regression on the portfolio and benchmark returns to calculate alpha and beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "863d6363",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = benchmark_returns.values\n",
    "Y = portfolio_returns.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "329b00ca",
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha, beta = linreg(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "004bcfa2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Alpha: 0.002638518577761206'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'Beta: 5.55121306008357'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(f\"Alpha: {alpha}\")\n",
    "display(f\"Beta: {beta}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c9d8cce",
   "metadata": {},
   "source": [
    "Plot the regression line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a96c2a6c",
   "metadata": {},
   "outputs": [],
   "source": [
    "X2 = np.linspace(X.min(), X.max(), 100)\n",
    "Y_hat = X2 * beta + alpha"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a6c7c71",
   "metadata": {},
   "source": [
    "Plot the raw data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "9b48d4ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Portfolio daily return')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X, Y, alpha=0.3)\n",
    "plt.xlabel(\"SPY daily return\")\n",
    "plt.ylabel(\"Portfolio daily return\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33055e26",
   "metadata": {},
   "source": [
    "Add the regression line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "275ae7a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X2, Y_hat, \"r\", alpha=0.9)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23d052b8",
   "metadata": {},
   "source": [
    "Construct a portfolio with beta hedging"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "8059feca",
   "metadata": {},
   "outputs": [],
   "source": [
    "hedged_portfolio_returns = -1 * beta * benchmark_returns + portfolio_returns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9363fc36",
   "metadata": {},
   "source": [
    "Perform linear regression on the hedged portfolio returns and benchmark returns to calculate alpha and beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "5574f4da",
   "metadata": {},
   "outputs": [],
   "source": [
    "P = hedged_portfolio_returns.values\n",
    "alpha, beta = linreg(X, P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "497a95a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Alpha: 0.0026385185777612072'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'Beta: -5.3398614836742606e-15'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(f\"Alpha: {alpha}\")\n",
    "display(f\"Beta: {beta}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a81552a",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "source": [
    "Define a function to calculate the information ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1079c198",
   "metadata": {},
   "outputs": [],
   "source": [
    "def information_ratio(portfolio_returns, benchmark_returns):\n",
    "    \"\"\"\n",
    "    Determines the information ratio of a strategy.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    portfolio_returns : pd.Series or np.ndarray\n",
    "        Daily returns of the strategy, noncumulative.\n",
    "    benchmark_returns : int, float\n",
    "        Daily returns of the benchmark or factor, noncumulative.\n",
    "    Returns\n",
    "    -------\n",
    "    information_ratio : float\n",
    "    Note\n",
    "    -----\n",
    "    See https://pyquantnews.com/how-to-measure-skill-portfolio-manager/ for more details.\n",
    "    \"\"\"\n",
    "\n",
    "    active_return = portfolio_returns - benchmark_returns\n",
    "    tracking_error = active_return.std()\n",
    "    return active_return.mean() / tracking_error"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a12584e8",
   "metadata": {},
   "source": [
    "Calculate the information ratio for the hedged and unhedged portfolios"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9ac1cedc",
   "metadata": {},
   "outputs": [],
   "source": [
    "hedged_ir = information_ratio(hedged_portfolio_returns, benchmark_returns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "fc39e40f",
   "metadata": {},
   "outputs": [],
   "source": [
    "unhedged_ir = information_ratio(portfolio_returns, benchmark_returns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "d8814e73",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Hedged information ratio: 0.019857076696277627'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'Unhedged information ratio: 0.030991554126598382'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(f\"Hedged information ratio: {hedged_ir}\")\n",
    "display(f\"Unhedged information ratio: {unhedged_ir}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3bd2158d",
   "metadata": {},
   "source": [
    "**Jason Strimpel** is the founder of <a href='https://pyquantnews.com/'>PyQuant News</a> and co-founder of <a href='https://www.tradeblotter.io/'>Trade Blotter</a>. His career in algorithmic trading spans 20+ years. He previously traded for a Chicago-based hedge fund, was a risk manager at JPMorgan, and managed production risk technology for an energy derivatives trading firm in London. In Singapore, he served as APAC CIO for an agricultural trading firm and built the data science team for a global metals trading firm. Jason holds degrees in Finance and Economics and a Master's in Quantitative Finance from the Illinois Institute of Technology. His career spans America, Europe, and Asia. He shares his expertise through the <a href='https://pyquantnews.com/subscribe-to-the-pyquant-newsletter/'>PyQuant Newsletter</a>, social media, and has taught over 1,000+ algorithmic trading with Python in his popular course **<a href='https://gettingstartedwithpythonforquantfinance.com/'>Getting Started With Python for Quant Finance</a>**. All code is for educational purposes only. Nothing provided here is financial advise. Use at your own risk."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0f3e1508-6ab5-4592-bcac-bebf4742ffa5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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